A second clue is provided by Cepheid variables. A Cepheid is a very special sort of star, which 'breathes' in and out all the time, getting fainter and brighter as it does so. It does this on a very regular pattern, which depends on its luminosity. We know that from observing those Cepheids which are close enough for us to be able to measure their parallax. From their distance and apparent brightness we can calculate luminosity. Luckily, we have found Cepheids in galaxies other than our own - and we can use that fact, and their apparent brightness, to work out how far away they are. This is an example of the 'standard candle'approach.
Another excellent standard candle is a Type 1a supernova. We know how they work, and they all work the same way, exploding very spectacularly, with very much the same force in every case (for excellent theoretical reasons - you can look them up if you like). Since a supernova can be as bright as the rest of its host galaxy, this is a technique which can work over very long distances. Again, measure the apparent brightness, and since we know the luminosity, we can calculate the distance.
These techniques allow us to calibrate the standard method for estimating very large distances in the universe, namely the Hubble red shift.
All these techniques, taking together, provide very compelling evidence that distant galaxies really are unimaginably distant.
Is that what you wanted to know?